Topic
Multiple-scale analysis
About: Multiple-scale analysis is a research topic. Over the lifetime, 1360 publications have been published within this topic receiving 27530 citations.
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TL;DR: In this paper, the authors investigated the instability of a single-machine quasi-infinite busbar system with the swing equation and showed that it exhibits period-doubling bifurcations, chaotic motions, and unbounded motions.
Abstract: We investigate some of the instabilities in a single-machine quasi-infinite busbar system. The system's behavior is described by the so-called swing equation, which is a nonlinear second-order ordinary-differential equation with additive and multiplicative harmonic terms having the frequency Ω. When Ω≈ω0, where ω0 is the linear natural frequency of the machine, we use digital-computer simulations to exhibit some of the complicated responses of the machine, including period-doubling bifurcations, chaotic motions, and unbounded motions (loss of synchronism). To predict the onset of these complicated behaviors, we use the method of multiple scales to develop an approximate first-order closed-form expression for the period-one responses of the machine. Then, we use various techniques to determine the stability of the analytical solutions. The analytically predicted period-one solutions and conditions for its instability are in good agreement with the digital-computer results.
47 citations
TL;DR: In this article, the non-linear response of a simple rigid disk-rotor supported by active magnetic bearings (AMB) without gyroscopic effects is studied under multi-excitation forces.
46 citations
TL;DR: In this article, the authors investigated the friction-induced instability and the resulting self-excited vibration of a propeller-shaft system supported by a water-lubricated rubber bearing.
46 citations
TL;DR: In this paper, the authors derived the governing equation from the generalized Hamilton's principle and discretized into a multiple-degrees-of-freedom system by the Galerkin's method, and investigated local and global resonances under the condition of 3:1 internal resonance of a super-critically axially moving beam, subjected to a harmonic exciting force.
46 citations
TL;DR: In this article, the coupled bending-bending vibration of a rotating pretwisted, tapered beam with non-constant angular velocity is investigated, and the effects of damping coefficient, pretwist angle and taper ratio on the changes of the boundaries of instability regions are also investigated.
46 citations